Tag: time in 24 hour clock

Questions Related to time in 24 hour clock

The hands of a clock coincide after every  $66$  minutes of correct time. How much is the clock fast or slow in  $24$  hours?

maths measuring time time in 24 hour clock time difference time

  1. $12 \frac { 108 } { 121 }$

  2. $11 \frac { 109 } { 121 }$

  3. $Both (A) & (B)$

  4. None of these

Show answer
Correct Option: B
Explanation:

The angle between $2$ successive numbers in the clock is $\dfrac{360}{12}=30^{\circ}$

The angle between successive dots is $\dfrac{360}{60}=6^{\circ}$
For one rotation of minutes hand hours hand rotates by $30^{\circ}$
$\implies $ For increase in $1$ minute there is increase of $\dfrac{1}{2}^{\circ}$ for hours hand
Net decrease For $1$ min is $\dfrac{11}{2}^{\circ}$
For $x$ min the decrease must be $30^{\circ}$
$\implies x=\dfrac{60}{11}$
So the hands to co incide again it takes $60+\dfrac{60}{11}\implies 65\dfrac{5}{11}$ min
The clock shows $\dfrac{6}{11}$ min error for $66$ min

The clock shows $x$ min error for $24\times 60$ 
$\implies x=\dfrac{\dfrac{5}{11}\times24\times60}{11}=11\dfrac{109}{121} $

Calculate the time shown on Varun's watch, when the actual time was half past $6$ in the evening.

maths measuring time time in 24 hour clock time difference time

  1. $5:30$ p.m

  2. $6:55$ p.m

  3. $6:30$ p.m

  4. $5:55$ p.m

Show answer
Correct Option: A
Explanation:
With minutes 1 – 29, we say it’s past (or after) the hour.

Therefore, half past 6 means

$5:30pm$

Choose the most appropriate option.
The angles between the hands of a clock when the time is $4:25$ am is?

maths measuring time time in 24 hour clock time difference time

  1. $14.5$ degrees

  2. $12.5$ degrees

  3. $17.5$ degrees

  4. $13.5$ degrees

Show answer
Correct Option: C
Explanation:
The hour hand rotates $0.5^o$ per minute while the minute hand rotates $6^o$ per minute.

At exactly four, the hour hand as completed $240$ minutes $= 120^o$. 

Hence angle between minute and hour hand at that point is $120^o$.

At $4:25,$ the minute hand has moved $25\times 6= 150^o.$

Thus angle between minute hand and $12$(on the clock) is $150^o.$

But at the same time, even the our hand has moved $0.5\times 25= 12.5^o.$

Now, the angle between the hour hand and $12$(on the clock) is $120+12.5=132.5^o$.

Now the angle between the two hands of the clock $=150^o-132.5^o$ 
                                                                                       $ = 17.5^o.$
                                                                       

Three bells in a temple toll at every $10$ minutes, $18$ minutes and $30$ minutes respectively. If they toll together at $7:00$ am , then the time among the following at which they will tool together again is 

maths measuring time time in 24 hour clock time difference time

  1. $1:30$ pm

  2. $2:30$ pm

  3. $3:30$ pm

  4. $3:00$ pm

Show answer
Correct Option: A

A clock is set at  $5{ am }.$  If the clock loses  $16$  minutes in  $24$  hours, what will be the true time when the clock indicates  $10$  pm on  $4 th$  day?

maths measuring time time in 24 hour clock time difference time

  1. $9:30{ pm }$

  2. $11 pm$

  3. $10 pm$

  4. $10:30{ pm }$

Show answer
Correct Option: A

Hari and Aman walk on a circular track and they take $120$ seconds and $150$ seconds respectively to complete one revolution. If they start together at $6:00$ AM from the starting point , then how many times will they meet between $6:05$ AM and $7:35$ AM?

maths measuring time time in 24 hour clock time difference time

  1. $6$

  2. $9$

  3. $12$

  4. $4$

Show answer
Correct Option: A

A person has mistaken the image of a clock in a plain mirror as the clock and read the time as 6:10. What was the correct time?

maths measuring time time in 24 hour clock time difference time

  1. 6:50

  2. 5:50

  3. 5:10

  4. 7:50

  5. None

Show answer
Correct Option: B
Explanation:

Assume that there is a line drawn between 12 and 6 on the clock, this can be a line of symmetry.
When we take the mirror image of this clock, the hands that are on the right side of this line will appear equidistant on the left side of the line and vice versa.
The time indicated is 6:10, the hour hand a little after 6 and the minute hand on 2.
Its mirror image will become, the hour hand a little before 6 and the minute hand on 10, i.e, 5:50.

A clock, which loses 5 minutes per day, is set to show the correct time at 12 noon on a Sunday. What time does the clock show at 12 noon on the next Sunday?

maths measuring time time in 24 hour clock time difference time

  1. 11 a.m.

  2. 12 noon

  3. 11.35 a.m.

  4. 11.25 a.m.

  5. None of these

Show answer
Correct Option: D
Explanation:

The clock loses $5$ minutes per day
in 7 days, time lost $=5 \times 7=35mins$
actual time $=12'o clock$,
time shown $=11:25 a.m.$

A clock is set to show the correct time at 11:00 a.m. The clock gains 12 minutes in 12 hours. What will be the correct time when the clock indicates 5:30 p.m. the next day?

maths measuring time time in 24 hour clock time difference time

  1. 5.00 p.m.

  2. 5.10 p.m.

  3. 5.20 p.m.

  4. 6.00 p.m.

  5. 5.48 a.m.

Show answer
Correct Option: A
Explanation:

The clock gains 12 mins in 12 hours,
It will gain 1 min in every 1 hour.
Difference in time the clock indicates=5:30 p.m.-11 a.m. (the next day)
=30.5 hours,
Time gained=30.5/1=30 mins.
Actual time=5 p.m.

There are two clocks on a wall, both set right at 10:00 a.m. One clock is losing 2 minutes per hour and the other clock is gaining 3 minutes per hour. If the clock which is losing 2 minutes per hour shows 3:00 p.m. the next day, what time does the clock gaining 3 minutes per hour show?

maths measuring time time in 24 hour clock time difference time

  1. 5.30 p.m.

  2. 4.00 p.m.

  3. 4.15 p.m.

  4. 5.00 p.m.

  5. None

Show answer
Correct Option: A
Explanation:

In each hour, the time difference between the 2 clocks will increase by 5mins
time passed $=24+2+3=29hrs$ on clock 1
Real time on clock $1=4 p.m$
difference between 2 clocks=$5*30=150mins$,
time on clock $2=3hrs+2hrs+30mins$
$=5.30 p.m$